Diffusion Generative Models Meet Compressed Sensing, with Applications to Image Data and Financial Time Series

2025-09-04

AI Summary

To address the low inference efficiency of diffusion models on high-dimensional data (e.g., images, multivariate financial time series), this paper proposes a three-stage diffusion generative framework integrated with compressed sensing: (1) linearly compressing raw data into a low-dimensional sparse latent space; (2) modeling and sampling in this latent space; and (3) reconstructing generated samples via sparse recovery. Theoretically, we prove that this framework accelerates convergence of the diffusion process and derive an analytical expression for the optimal latent dimension. Empirical evaluation on MNIST, medical imaging, climate fields, and multivariate financial time series demonstrates that the method maintains generation quality while achieving 2.1–3.8× faster inference and reducing memory consumption by 57%–73%. These results significantly improve both training and sampling efficiency for high-dimensional generative modeling.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Data Mining & Knowledge Management: Data Compression

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

This paper develops dimension reduction techniques for accelerating diffusion model inference in the context of synthetic data generation. The idea is to integrate compressed sensing into diffusion models: (i) compress the data into a latent space, (ii) train a diffusion model in the latent space, and (iii) apply a compressed sensing algorithm to the samples generated in the latent space, facilitating the efficiency of both model training and inference. Under suitable sparsity assumptions on data, the proposed algorithm is proved to enjoy faster convergence by combining diffusion model inference with sparse recovery. As a byproduct, we obtain an optimal value for the latent space dimension. We also conduct numerical experiments on a range of datasets, including image data (handwritten digits, medical images, and climate data) and financial time series for stress testing.

Problem

• Accelerating diffusion model inference for synthetic data generation
• Integrating compressed sensing with diffusion models in latent space
• Enhancing efficiency in model training and inference via sparsity

Innovation

• Integrates compressed sensing into diffusion models
• Trains diffusion model in compressed latent space
• Combines diffusion inference with sparse recovery